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6.002 Spring 2020 Lecture 21 1

6.002 CIRCUITS ANDELECTRONICS

Lecture 21 – MOSFET, MOSFET amplifier

April 30, 2020

Contents:1. Review of amplifiers2. MOSFET i-v characteristics3. MOSFET amplifier4. Small signal response (probably next week)

Reading Assignment:Agarwal and Lang, Ch. 7 (§§7.3-7.6)

Handouts:Lecture 21 notes

Announcements:This lecture is being recorded and it will be posted in the certificates-protected part of the 6.002 website

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1. Review of amplifiers• In the past, we studied this circuit:

• Transfer characteristics:

Circuit behaves as amplifier if: RLG>1

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• Key device needed to make an amplifier: voltage-controlled current source

• Is there a device that exhibits this behavior?

Yes! The MOSFET! (and other transistors)

Ii

Iv

Oi

Ov+

–

+

–IGv

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4. Transistors… The MOSFET• MOSFET=Metal-Oxide-Semiconductor Field-Effect Transistor• MOSFET=three terminal semiconductor device• In the MOSFET: Current through two terminals (source and drain)

controlled by voltage in third terminal (gate).• Two different kinds: n-type and p-type conduction• A modern microprocessor contains ~109-5x109 MOSFETs

Inte

l 14

nm

MO

SFET

8 nm

Samsung 14nm MOSFET

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How does a MOSFET work?

http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/mosfet.htmlhttps://www.youtube.com/watch?v=tz62t-q_KEc&start=230

Demo

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https://www.researchgate.net/figure/FET-Conventional-symbol-types_fig3_277095691

And many more…

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Julius Lilienfeld and the first MOSFET

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https://www.computerhistory.org/siliconengine/field-effect-semiconductor-device-concepts-patented/

The first transistor (1947)…

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http://www.computerhistory.org/revolution/digital-logic/12/273/1364

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https://mixedsignal.wordpress.com/2015/12/14/the-transistor-symbol/

https://hackaday.com/tag/point-contact-transistor/https://www.elprocus.com/different-types-of-transistor-and-their-functions/

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1947: John Bardeen and Walter Brattain, with support from colleague William Shockley, demonstrate the transistor at Bell Laboratories in Murray Hill, New Jersey.

AB

C

6

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Three regimes of operation:– Cut-off: vGS≤ VT

iD=0

– Linear or triode: vGS>VT, vDS≤ vGS-VT

iD depends on vGS and vDS

– Saturation: vGS>VT, vDS≥ vGS -VT

iD depends only on vGS

MOSFET i-v characteristics

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• MOSFET as voltage-controlled current source ( ~analog electronics):

• MOSFET as switch ( ~digital electronics):

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MOSFET equations

– Cut-off: vGS≤ VT

– Linear or triode: vGS>VT, vDS≤ vGS -VT

– Saturation: vGS>VT, vDS≥ vGS –VT

Two parameters characterize the MOSFET in this simple model:

– Threshold voltage: VT (in V)– “K factor”: K (in A/V2)

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• Compare behavior of MOSFET in saturation with that of voltage-controlled current source:

• In MOSFET in saturation, the gate-source voltage is the control voltage.• Key to make MOSFET amplifier: use MOSFET in saturation!

iO

vO

vI

I=GvI

00

8

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3. MOSFET amplifier• In analogy with:

• Consider this circuit:

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• How does it work?• Use graphical technique first:

àdraw “load line” associated with RL

• Operating point of amplifier at intersection of load line with MOSFET characteristics.

Vo=VS-RL.iD

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• Sketch the transfer characteristics:

• When MOSFET in saturation, transfer characteristics steep à high voltage gain!

Vo=Vs-RL.iD

Demo

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• High voltage gain region suitable for amplifier:

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• Cutoff and linear regions unsuitable for amplifier: low gain and distortion

Demo

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• In saturation, MOSFET operates as current source à equivalent circuit:

How to quantitatively calculate transfer characteristic?

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• Amplifier transfer characteristics:

Node equation for node vO:

Then, transfer characteristics:

Note: transfer function is quadratic à distortion!!

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4. How to minimize distortion: Small-signal

• Transfer characteristics of MOSFET amp are not linear:

à distortion!

• Key insight: if magnitude of signal is small relative to VS, transfer characteristics around bias point look fairly linear à low distortion.

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• If one can linearize, what are the vo-vi small-signal transfer characteristics?• Large-signal transfer characteristics:

• Input is of form:

• Output should then be of form:

• Identify terms:– Bias terms:

– Small-signal terms:

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• Small-signal terms:

• Linearizing means keeping only the linear term:

• Small-signal gain:

slope: -KRL(VI -VT)

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• When is this approximation good?

quadratic term << linear term

Or:

• The higher the bias, the easier it is to deliver this condition.

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• Let’s put some numbers: use 2N7000 (VT=2 V, K=0.14 A/V2)with RL=250 Ω and VS=5 V.

Transfer characteristics look like:

If select VO=2.7 V, then VI=2.4 V, and:

Input waveform with Vi=80 mV [≈0.2(VI –VT )], gives output waveform with Vo=1 V.

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• More generally, obtain small-signal transfer characteristics by Taylor series expansion of large-signal transfer characteristics.

• If large-signal transfer characteristics are:

• Then, if vI=VI+vi, expand around (VI,VO):

• Small-signal transfer characteristics are:

• And small-signal gain is:

[check that from here, you get the same result as above]

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Summary

• Three regimes of operation to a MOSFET: cutoff, linear and saturation

• In order to make an amplifier, MOSFET must be used in saturation• A simple MOSFET model provides adequate description of i-v

characteristics and requires only two parameters:– Threshold voltage– “K factor”

• An amplifier can be constructed with one MOSFET and one resistor. • Transfer characteristics are quadratic (some degree of distortion

introduced)